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Last year, Company X paid out a total of $1,050,000 in salaries to its

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Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 20 Apr 2015, 07:53
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Question Stats:

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Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000


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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 21 Apr 2015, 09:44
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Bunuel wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000


Kudos for a correct solution.


Let's imagine that \(x\) is max salary and \(\frac{x}{1.2}\) is min salary.
As we know that total amount of salary equal to 1,050,000 we can write equation:
\(20x+\frac{x}{1.2}=1,050,000\) (20 employees with max salary and one with min salary: if we take 20 employees with min salary we will receive bigger number and as we need least possible salary we should take 20 max salaries)
\(24x + x = 12,600,000\)
\(x = 50,400\) and this is max salary
\(50,400 / 1.2 = 42000\)

And our answer is C
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 21 Apr 2015, 21:41
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Hi All,

This question is remarkably similar to the following Official GMAC question:

a-certain-city-with-a-population-of-132-000-is-to-be-divided-into-11-v-191085.html?hilit=population%20GREATEST#p1464387

The various methods to solve it are exactly the same (including the opportunity to TEST THE ANSWERS).

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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 22 Apr 2015, 05:56
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Assume the \(21^{st}\) guy receives the lowest salary \(x\)
and everybody else receives \(x+\frac{20}{100}x\) salary
\(x\,+\,20*(1.2x)\,=\,$10,50,000\)
\(x\,+\,24x\,=\,$10,50,000\)
\(25x\,=\,$10,50,000\)
\(x\,=\,\frac{$10,50,000}{25}\,=\,42,000\)

Answer C
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 22 Apr 2015, 06:36
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Let x be the minimum salary,

Therefore, the maximum salary would be x * 0.2 + x = 1.2x
To get the minimum value for x, we have to maximise the value of all the other salaries, therefore we make all the other 20 people earn 1.2x

Total Amount
So we have x + 20(1.2x) = 1,050,000
x+ 24x = 1,050,000
25x = 1,050,000
x = 42,000
Answer choice C
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 22 Apr 2015, 09:55
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[quote="Bunuel"]Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000

Employee 1 earned $x(say)
Employee 2 will not earn more than $1.2x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees
(1.2x*20)+x=1,050,000
Solving for x=$42,000
Answer C
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 27 Apr 2015, 03:53
Bunuel wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Here ask yourself the following questions:

1) The numbers do not have to be integers.

2) Zero is theoretically possible (but probably constrained by the 20% difference restriction)

3) Numbers absolutely can repeat (which will be very important)

4) What’s your strategy? If you want the LOWEST possible single salary, then use your answer to #3 (they can repeat) and give the other 20 salaries the maximum. That way your calculation looks like:

x + 20(1.2x) = 1,050,000

Which breaks out to 25x = 1,050,000, and x = 42000. And notice how important the answer to #3 was – by knowing that numbers could repeat, you were able to quickly put together a smart strategy to minimize one single value.

The larger lesson is crucial here, though – these problems are often (but not always) fairly basic mathematically, but derive their difficulty from a situation that limits some options or allows for more than you’d think via integer restrictions, the possibility of zero, and the possibility of repeat values. Ask yourself these four questions, and your answer to the first three especially will maximize your efficiency on the strategic portion of the problem.
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 23 Jan 2016, 03:50
Back-solving.

Use answer D: if minimum is 50k then 20% greater than that is 60k. Calculate whether the total salary base matches with that: 60*20+50 = way too much.

Use answer A (B is ugly so let us leave it for now): 40 + 48*20 = 1000 -> too little

Let us test C (B is ugly): 42 + 42*1.2*20 = 1050. Bingo!
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 06 Feb 2018, 18:36
Bunuel wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000


Since the sum of all the salaries is a fixed amount (which is given to be $1,050,000), the lowest possible salary is obtained when all the salaries besides the lowest one are maximized. Since the greatest possible difference between any two salaries in this company is 20%, all the salaries besides the lowest salary should be 20% more than the lowest salary.

We can let the lowest salary = x and the greatest = 1.2x and create the following equation:

x + 20(1.2x) = 1,050,000

x + 24x = 1,050,000

25x = 1,050,000

x = 42,000

Answer: C
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 14 Apr 2018, 02:51
Tmoni26 wrote:
Let x be the minimum salary,

Therefore, the maximum salary would be x * 0.2 + x = 1.2x
To get the minimum value for x, we have to maximise the value of all the other salaries, therefore we make all the other 20 people earn 1.2x

Total Amount
So we have x + 20(1.2x) = 1,050,000
x+ 24x = 1,050,000
25x = 1,050,000
x = 42,000
Answer choice C



Dear Tmoni26,
You've explained the logic very concisely, clearly & perfectly.
Made perfect sense & helped me understand in least possible words.
Thank you!

Regards,
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 02 Oct 2018, 00:49
Quote:
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000
This is a min/max problem can be attacked several different ways.
If the goal is to find the minimum possible salary among the 21 employees then you want to maximize the salary of 20 employees and see how much is left for the one remaining person with the lowest salary.

Since no salary can be more than 20% greater than any other, you want to assign the low salary as x and the remaining 20 salaries as 1.2x (20% greater than x).

The total salaries would then be x + 20(1.2x) = 25x. Dividing $1,050,000 by 25 you see that the lowest salary would be $42,000
the correct answer is (C).

Alternatively:
Quote:
Also on this problem, you could back solve using the same logic: start with C and multiply it by 1.2 to get $50,400.

If you multiply $50,400 by 20 and add $42,000 you get the required total of $1,050,000.

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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 22 Oct 2018, 01:35
I am still not sure why we are taking 20 with max salary and 1 with lowest salary. By any means the max difference can come even if we take 1 person with max and 20 with min.
But with this, the answer changes. Could someone please help me with this.
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its  [#permalink]

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New post 22 Oct 2018, 02:06
asthagupta wrote:
I am still not sure why we are taking 20 with max salary and 1 with lowest salary. By any means the max difference can come even if we take 1 person with max and 20 with min.
But with this, the answer changes. Could someone please help me with this.


Hi asthagupta,
https://gmatclub.com/forum/a-certain-ci ... 76217.html

Please check the explanation of Bunuel in the above link(OG Question), you may raise further specific queries (if any).
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its   [#permalink] 22 Oct 2018, 02:06
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